Proposition 4.6 (Lemma 12.2.2 in [1]}, see also Proposition 1.15 in [2]}) 
Fix \(\alpha ,\beta \in \mathbb {N}I\)  and \(I\) -graded vector spaces \({\mathbf {V}_{\alpha }},{\mathbf {V}_{\beta }},{\mathbf {V}_{\alpha +\beta }}\)  with dimension vectors \(\alpha ,\beta ,\alpha +\beta \) , respectively.
For semisimple complexes \(A\in {\mathcal {D}}_{G_{\mathbf {V}_{\alpha }}}^{b,ss}(E_{\mathbf {V}_{\alpha }})\) , \(B\in {\mathcal {D}}_{G_{\mathbf {V}_{\beta }}}^{b,ss}(E_{\mathbf {V}_{\beta }})\)  and \(C\in {\mathcal {D}}_{G_{\mathbf {V}_{\alpha +\beta }}}^{b,ss}(E_{\mathbf {V}_{\alpha +\beta }})\) , we have
\(\lbrace A\ast B,C\rbrace =\lbrace A\boxtimes B,\mathrm {Res}^{\alpha +\beta }_{\alpha ,\beta }(C)\rbrace .\) 

